A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \text{ m}^2$$ and resistance $$100\Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$B = 0.5 \text{ T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \text{ s}$$ is ______ $$\times 10^{-8} \text{ J}$$.

$$\text{Side length of the square loop: } l = \sqrt{A} = \sqrt{3.6 \times 10^{-3}}\ \text{m}$$

$$\text{Since it is pulled out in time } t\text{, the velocity is: } v = \frac{l}{t} = \frac{\sqrt{A}}{t}$$

$$\text{Induced EMF: } \varepsilon = N B l v = N B \sqrt{A} \left(\frac{\sqrt{A}}{t}\right) = \frac{N B A}{t}$$

$$\varepsilon = \frac{10 \times 0.5 \times 3.6 \times 10^{-3}}{1.0} = 1.8 \times 10^{-2}\ \text{V}$$

$$\text{Total work done: } W = \frac{\varepsilon^2}{R} \cdot t = \frac{\left(1.8 \times 10^{-2}\right)^2}{100} \times 1.0 = \frac{3.24 \times 10^{-4}}{100} = 324 \times 10^{-8}\ \text{J}$$